Chapter 6 Game-Theoretic Foundations

6.1 Games in extensive and strategic forms
6.1.1 Games in extensive form
6.1.2 Games in strategic form
6.1.3 Transformations between
strategic and extensive forms
6.2 Randomized strategies: mixed, behavioral and general
6.2.1 Mixed strategies
6.2.2 Behavioral strategies
6.2.3 General strategies
6.3 Equivalence theorems for linear games and games of perfect recall
6.4 Implications for competitive analysis
6.5 Historical notes and open questions
6.5.1 Open questions

Chapter 10 The $k$-Server Problem

10.1 The formulation of the model
10.2 Some basic aspects of the $k$-server problem
10.2.1 The optimal
offline algorithm
10.2.2 The greedy
policy is not competitive
10.2.3 Lazy algorithms
10.2.4 Some generalizations
and variants of the server problem
10.2.5 The $k$-server
conjecture
10.3 A deterministic lower bound
10.4 $k$-servers on a line and a tree
10.4.1 The line algorithm
10.4.2 The tree algorithm
10.4.3 Some applications
of the tree algorithm
10.5 A 3-competitive 2-server algorithm for Euclidean spaces
10.6 Balancing algorithms
10.7 The $k$-server work function algorithm
10.7.1 Work functions
for the $k$-server problem
10.7.2 The online
$k$-server work function algorithm
10.7.3 Analysis of
algorithm WFA
10.8 On generalizations of the $k$-server conjecture that fail
10.8.1 The $(h,k)$-server
problem
10.8.2 Asymmetric
spaces
10.9 Historical notes and open questions
10.9.1 Open questions

Chapter 11 Randomized $k$-server Algorithms

11.1 Two randomized $k$-server algorithms for the circle
11.1.1 A $2k$-competitive
algorithm
11.1.2 A circle algorithm
with sub-linear ratio
11.2 A lower bound against an adaptive online adversary
11.3 The cat and rat game and applications to randomized $k$-server algorithms
11.4 The Harmonic algorithm
11.5 Randomized algorithms for Resistive spaces
11.6 Historical notes and open questions
11.6.1 Open questions